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Tree data structures for N-body simulation

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1 Author(s)
R. J. Anderson ; Dept. of Comput. Sci. & Eng., Washington Univ., Seattle, WA, USA

In this paper, we study data structures for use in N-body simulation. We concentrate on the spatial decomposition tree used in particle-cluster force evaluation algorithms such as the Barnes-Hut algorithm. We prove that a k-d tree is asymptotically inferior to a spatially balanced tree. We show that the worst case complexity of the force evaluation algorithm using a k-d tree is Θ(nlog3nlogL) compared with Θ(nlogL) for an oct-tree. (L is the separation ratio of the set of points.) We also investigate improving the constant factor of the algorithm, and present several methods which improve over the standard oct-tree decomposition. Finally, we consider whether or not the bounding box of a point set should be “tight”, and show that it is only safe to use tight bounding boxes for binary decompositions. The results are all directly applicable to practical implementations of N-body algorithms

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996